Sometimes people say that water is removed from clothes in a spin dryer bn/b :;fn+xx:w e*lw ohy centrifugal force thxn x ;e:n/:w f*wbl+ohrowing the water outward. What is wrong with this statement?

Will the acceleration of a cary r3cc pfmz6zju3 dt90mm5c5. be the same when the car travels around a sharp curve at a const.cj6m9 m3y z5z5 0 cfdmcu3rptant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed apo 9 f,efp5-7 i2hghe*bviwx-m 5fr n5long a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a5g 5e- v*hpf-57,fo 9bnrwm2xhifepi hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-rou uw;;womg .jt3nd. Which of these forces provides the centripetal ag;wwu .; mjto3cceleration of the child?

A bucket of water can be whirled in aqf iewyr8zs0++; to,m vertical circle without the water spilling out, even at the top of the circle when the bucket is upwrtzef+qo ;m+8yi 0,sside down. Explain.

How many “accelerators” do you have in your car? There are at leacz-om* zgdp()0aj:hx st three controls in the car which can be used to cause the car to accelerate. What *pzmdhj (:o0)c- xagzare they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shoe83kwgh/-e68t l 6uli vyem7uwn in Fig. 5–31. His sled does not leave the ground (he does not achieve “air7l 66hk e u8-3tuv8we/giem ly”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riderp 6mhwr5:2y 6)d/qn zkygzc(z s lean inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How1,1ks4 qut+qde bry 5t would you compute the banking angle given its spee utby ,+s4eqd51 kr1tqd and radius of the turn?

A girl is whirling a ball on a st(xzltf:9x1 bering around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side o:e 1(x xtblfz9f the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? Ik+skk; f*,azmf so, how large a force? Consider + ,sz*kmka fk;an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what ita() *d q+uit 8:.6 mthflvsibx is, in what ways would the Moon’s orbit be different?i tmdubl:fiqx6t + (v8a*)h.s

Which pulls harder gravitationally, the Earth on the Moon, or tsrjws ve w( d gv5l(-;g18ie7fhe Moon on the Earth? Whic;1(ilfw5ve w8 vj7 g dr-gses(h accelerates more?

The Sun's gravitational pull on the Ear +-py:vx )hjglth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational-p:+xvj gh yl) pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at th+z(qo2 xu8uqc )ub eq*e poles? What two effects are at work? Do they oppose qbqu(zec)uuq8x o+*2 each other?

The gravitational force on the Moon due to the Earth is only aboua49y k2eq7n9rd rk1l st half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from thq9rn2rkl7kae dy9s1 4e Earth?

Is the centripetal acceleration orc+o:av(0q yt f Mars in its orbit around the Sun larger or smaller than the ce+yoca(0vt qr:ntripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) tj+p7fjpsu6c uumu . a-r tx//,oward the east or (b) toward the west? Consider the Earth’s rotation dirajrm +7/u-.t,jsc/xu fu6p puection.

When will your apparent weight be the greatest, as measured by a scalehi 09s xjb.o8x.4bucf in a moving elevator: when the elevator (cx hojx904 b.uis8fb.a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affec:,04:(v 2:efo lqommpym.uurnin eu+ted by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the forom e: m:0 2npo:u(yeilmu+rvf4 . u,qnce we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “freab7 p4-rg+(jftraez x l2pr77 e fall” or “apparent weightlessness” between steps.gr (ra47 p tr z7bf7ea2px+j-l

The Earth moves faster in its orbit around the Sun) ;nde4h eac sfdw7-s1 in January than in July. Is the Earth closer t s ;dwse-71dc )4ehanfo the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discover p:cvqbmji28 hs)1 5)j:x nd.knsube2ed to have a moon. Explain how this discoveb)s 52kxjj mhnb spv1nu8c):. :2ieqdry enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger thaj5nr:rpoz kq 8r34(h4h:vyd6 c evu5p n the Moon's. Yet the Moon's is ma cury6h44z5jeq:vo hp8kpv : dnr3(r 5inly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 6h s3um pbnm- u(sk(: u:srf,k1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the d p*ven/n (1u kxecnz;-6 ;qcwEarth in its orbit around the Sun, and the net force exerted on the Earth. What exertsn/ee n pwvu(;kd1x-c6*qcn z; this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exr l y7uwm2 c.ks(9d+mnerted on a 2.0-kg discus as it rotates uniformly in a dm+ ysm lkc7u.9(2wrnhorizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the 1dmc+xkbd,l bua1n e8;yo 1*e Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Eaou kd,c +b;nyb e* el11xd1a8mrth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of a c1 )xzq 6b+oc.dh;.u jsvg:j xpotter’s wheel turning at 45 +xqcjogvs1:h;.dj) b cx uz6.rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revo1c--zcc)h 22tmvvde klved at a uniform rate in a vertical circle of 2v2mcek1) vzhcdt c--radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-kg car can round a turn of radius 77zpnx98g/m+g,bb z a+b u m-g)e m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mae 89-ggab uzzx ,g pmnbb+m/+)ss of the car?   

  How large must the coeffig- ci)1 ,xbr0 vza1ofqcient of static friction be between the tires and the r)fizxv a,o rb0 g-cq11oad if a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilo :sopk7xqh8tm;5z;e q rj2o-cot,f c 7ts is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on herp5 ;cmqo 2 8q: -7zocfo7etx s;h,jtkr back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the a5tl9.yy8l io s 9kegtlr04 (pbxis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction betweeier59 tlgby pl t4.yl(so089kn the coin and the turntable?   

  At what minimum speed must a roller coastehn*vkuw ;t7 *xr be traveling when upside down at the top o7hk;**nt xw vuf a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosswms+t( c cp(c5es the rounded top of a hill (radiu(wp s(+c 5ctcms =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute wouldl*j g*g c(-xks a 15-m-diameter Ferris wheel need to make for the passengersscjk* x -g(*lg to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirlewz :wha,vv)b *d in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in thewh, vb:v)z aw* rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.006mxfj(*0jy 4qorl5 vm cm from the axis of ro(*jlmjqory 06 4mx5fv tation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a cev ja ct78,g5aarnival, people are rotated in a cylindrically walled "room." (Seej,a7 e v5gcat8 Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-lqtug 5s-1; eahockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) ttug5e;l saq -1hrough a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by not ig7iwu8 jnpdy9krbg z.-a 08s;e noring the weight of the ball which revolves on a strij p gy9azse07i;u-r8.b8kdn wng 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88za6zfn i tz-+1 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of massesd;k 4vd ghl5w4 $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving ve.af ,k; ,tonha wwp;f.rtically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal cokx; 5t1fkz(9:qa8xwu +b gioomponents of the net force exerted on the car (by the gr( t9qa;gxoo8+ bz51kfk uwx :iound) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area, going f(ex ebpb w):o:rom rest to 320km/h in a semicircular arc wit)(x:e:eopbb wh a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particular in+jnthu80h x+zstant, its+n+0hxuj8h z t acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Earth radiips5e*dyd3 zv 4(-dq jp)j vys4-q*( d3pepd5d z above the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certainu) mb(pxx qq.y .)q8cx2 sxi9 z0*bxqn planet, the gravitational acceleration g has a magnitudy)9xn m q.up qzb0( x*qq.8ixxxbsc2 )e of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravig tul aef) lbes1/d);4ty on the Moon. The Moon's radius is 1.7fubelag4);e l /s1 t)d4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times thhx(u l8l vvdig xc0/d:xh8(/d 0nn1g eat of Earth, but has the same mass. What id1v (lh 88x0u:/0n/x eig (lvcdgxndh s the acceleration due to gravity near its surface?   

  A hypothetical planet has a masse*whro 2qn2/ a 1.66 times that of Earth, but the same radius. What is g nearw h/ro2*qa2 ne its surface?   

  Two objects attract each other gravitationally with a forc z5,hn;fa y4dre of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, at :;h 3idhso dt5(a) 3200 m ds 5:o;th ihd3   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’swe-uer; qkbt/x55 i5f center to a point outside the Earth where thegravitationa5 5x /kqre-ubf;ew5 til acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a sphm/jpscei3v b-15v9e oere about 10 km in radius. Estimate the surface gravito- vi5 s/vcjb 9mee1p3y on this monster.    $\times10^12$

  A typical white-dwarf star, which once.x6dpl1t;nga1 8u vz z was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the 6z;.1zvudl8na pxtg1 mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless wme b xf;(9nbrige3a(at kr0,8hile orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravitx3i(t amb9 ;ern ge,rk0b8( afy 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.647yd:ijam 9/y2h/bz /ez1eg yc; bthc0 m. Calculate the magnitude and dir4i7yjzt b1;ygm//yh9ec d ebahz/ :2cection of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the sagm9 c f*ylfa94xzrx7 8:7 sqlzme side of the Sun. Calculate the total force on the Earth due to Venus, Jupi * gzlr 99mlxyqzx7f afs47c:8ter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceler78xaw-mt-u lrcu ww5-ation of gravity at the surface of Mars is 0.38 of what it is on Earth, anc7au8wwl-x - 5umt-wr d that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using thg*xc.e/nyn3yhc(z23 t *tsp:a vna m *e known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained n vyn mpyxe: ana3.2(*sz3 *gtc/ht*cusing Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stab22 zgs)lr. uim;:6gn66gn ju wavn:fw le circular orbit about the Earth at a hefnw6. i6 ng;s:ul6 g:m2uv zrgan wj2)ight of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a 3:po vvc1b r80ipgomjh31k c2circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) whenr:1jpo1k33mvvc p0 g8ihbo2 c the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experieny*8fuqnn :jb3u. ut.w ce simulated gravity of 0qu3.: utj *8.ynfnw bu.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a v1xy ovw-so7q u5g 37jsatellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the maw7 ogsqy1537ujx v-voss of the satellite?    s ~    min

  At what horizontal velocity would a satellit* 37roxve:en23t hli,urg;veh0m;g ie have to be launched from the top o eu;2 :hrexnvi *omi0 3tg,er3g;vlh7f Mt. Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command mod;ab at1sjqp1 w 9fh-w3ule continued to orbit the Moon at an altitude of about 100 km. How long did it take to t-h;pfjaw3s w 9aq1b1 go around the Moon once?    s

  The rings of Saturn are compos0x cahu4av35-9ct/, sdty xried of chunks of ice that orbit the planet. The inn5,/s 3aaxcv-rc 09yudht4xit er radius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. 5–9). W4q usmx :.en+what is the ratio of a person’s apparent weight to her real weixw +mq4s :en.ught (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from thpse xg8 uw;sy.f+;w5ub31g v xe center of the Earth' ;b +g s 1;f3xyvwu8sepugxw5.s Moon in a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system cons-r0yob3f 3jkzj*9 tdm ists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midj3-*br0yz3om fd9 jk tway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a xmu:+9s9 lslb55-kg woman in an elevator that9s: mll+bus9x moves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an elevatk m;n )lbsb;ru-:wbg 2or. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum a2ns kbb: m)bl;-wu;gr cceleration (magnitude and direction)? a =   

Show that if a satellite orbits very ng (;z6iulfr sgu:, z:year the surface of a planet with period T , the density (mass/volume) of the pla,y:z6i(z fr;lgs uug: net is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the pl hiaf /nf6.2edfb 6w/eriod of the Moon (27.4 d) to determine the period of an artifiw62beifnf//a 6.dlfh cial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a ncknoc)yx 1mt4 +n )2rfew hundred meters across, orbits the Sun like the planets. Its period is 410 )r)1x 4nko 2yncm+n ctd. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance g-z ru/n y11u3fi *awtof 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbitujjr21 gow4p f 1*)laes the Sun roughly once every 76 years. It comes very close to theojj 24ulfgw*)a1 epr1 surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the3 3hri /htecdam3 mxm(t,y* ,e center of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the (zyhz*+/ s+-bjr3dcfn rup(zfour largest moons of Jupiter (those discovered by Galileo in 1609).yf* r/n d+(zc3 rbh-z(s+puzj
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known perbhl ,jv8z/*h riod and distance of the Moon. zvrhj bh, *8l/   $\times 10^{24}$

  Determine the mean distancmzr8 kd;znnjom rqw/ 20/ *4owa4xdu0e from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare t0w/;mr d8m jzrnq20 *zu4aw/ oxkdn4o o the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupite,p x/n8b nk:ez3z9bcb r consists of many fragments (which some space scientistsb bz:z9,3 bc8nxnkpe/ think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of a bacit ic..(rdtq 2nk )g-t/qud1 nd completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on /.-2 ki(dt ntq qccdrg.1ui)tEarth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an az-+x 8f9damg( z2 wvxprc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can t+82(dwzgxxf9pzva m- olerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleiwcb9-z sh:h: ration of gravity be half what it is on t9 :c-ib zhwh:she surface?    $\times 10^6$

  On an ice rink, two skaters of equalfs:u 4 r.g)a4hzt6hhz n2zc8bw45 eux mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individuas w: u)rgtbhx4h2 .ea846czf5z z n4uhl masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once t/ 1edy)l(ilsper day, the apparent acceleration of gravity at the equator is slightly less than it would be if the E/ys(ilt)e1ld arth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directlyqz ;tp x0;qd1f 8uq,:/j gxhhe from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces? q1f;tp 8/: hx qxz d,j0qu;geh   $\times 10^8$

  You know your mass is 65 kg, but when yo i)ygi4rq- qmmzod5 - :yqk1,qu stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is tm 1ymyq-i),:q4rd-o iq g qz5khe acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space statiop-we8 c1yz0jbvf+ca(z* *uhin consists of a circular tube that will rotate about its center (like a tubulazw v- jpcb+(e1f0zyuc h 8a*i*r bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a rl hu)jgxmr(0n.9u3n vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the ma4;tvm pfstbrz2ie,58ss of a planet in terms of its radius r, the acceleration due to gravity at its surface and bt,f i8rev4z;s 5mt2p the gravitational constant G.

A plumb bob (a mass m hanging on a string) is d* vaw-g ad(1j.zone b0eflected from the vertical by an an 0 z(n-ow.bd*aeg1javgle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the coefficientmkv.ojhhl .y--8y +zu of static friction is 0.30 (wet pavement), at what range of speeds can a car safely hanvj kmy+.- yhu.l8oh- zdle the curve?

  How long would a day be if the Earth were rotating so fast that objects at thpx4katxzoy )b*0o.g 4j k6w2a hp4 le:e equator were apparentltk:oyx)2 xhp 4*4. l6wbae0oa kgpz4jy weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant p9bpeo: /6no yd z21jx5n1 cdedistance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant sp,vg,o) -ykb k5sl/exoeed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings ok,lv5goey x-)/sbo ,kut to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Th;am+* z nhnqgu/;pg(4xhx;)b vtpt 8 tus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following datqxt;mtnx ;h+g4b gvunhp;)*/azp (8 t a for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduce88qv3d -cy jt5rh2idwd the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring thcj38rvt d25diq8 w-yhe speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it td)s4n. u)w r a-c yf*tg;5kpzrt cq/.uraverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Sc u4/c)a)yk r*w;.g st.q-ftr pn5duzmallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioningzonj lrb7/1 4e System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of appr1 brzeln /7jo4oximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 bill ts 3slrplm9qaq8ybv 3d/ .::jion km, is meant to orbit the asteroid Eros at a height of about 15 km . Elvr: 3yas89lj q:pqt/ 3.mdbs ros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuin*cb6gd47jhj 3p m l3elg a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the E*hcgjb6jm43 7lle3p darth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its me,c f9d 7pp:/ ,xbzaqmj*+f1peylfj* man distance from the S1*e/ca*:yq jfp m p,9,+xf7z bmd plfjun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if yo48j6y95kit5mpr ar ap 7rna.d u could actually "feel" yourself gravitpnt yr48m5par 7r9a.5 ijak6dationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the centervnfltkbd -ita/o.xe /tvmk/((:g 2( m of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from t/ /(xi (tftb:dok2a vel-m.g /nm(vk the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at u i3jq3po0+z+7g jglx l)xb f*the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square. o0j3 qi 7)x+zuj xg3gl*+fpbl    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Eartt.bd j;zs*apj (e 3xlu76f ssbtb,10bh $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experi)xgiwq um( vnz927+w jixrt ;x-f; 1moenced by the tip of the 1.5-cm-long sweep second hand on your wris x)io(2qrj7x1ug nm +wx9 miwvt;z-;f t watch?    $\times 10^{-4}$

  While fishing, you get bored and start to 76 wguqy9 mns.wnm0b e3+gwj3 swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makesnq ws.90wg3j6m 7 m gnwe+ub3y a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new hitd(p:e( vs m8yb: zmby 56dvb h)v4nz*ghway is designed so that a car traveling a 8*6) m5pm(yvnhv:ydbzt 4bs :v( ebzdt speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utwx a+ qk662blrs o/k.dilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main forclk/dx + rsa6.ow 6bqk2e exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$